Hi, First point is whether you actually swallowed or it is just a notion. This can be confirmed by a simple x-ray of chest and abdomen. If confirmed, swallowing of crown is an emergency as it may get aspirated in lungs or may go into stomach. You should inform your dentist as soon as possible. As it has attach metal, it will be clearly visible and treatment options(if required) may depend on the same. The treatment options are- wait and watch for getting it paased out in 24-48 hrs with follow-up x-ray. if it is in the throat region then it can be retrieved with endoscope. take care!
A Few days..... must be careful .... make sure you kee an eye out so it doesnt cause problems